Talk:BOX M̃
I have discovered a truly marvelous proof that BOX_M~ = gigoombaverse, which this talk page is too small to contain. FB100Z • talk • 02:24, February 14, 2013 (UTC) :If that was proven, then a direct consequence is that BOX_M~ must have all the bizarre properties of Graham's number and then some. -- I want more 04:43, February 14, 2013 (UTC) Not looks like that. Despite that both numbers are "salad", gigoombaverse is defined using busy beaver function, but BOX_M~ is completely computable. I found that BOX_M~ < {3,5,2,1,2} in BEAF, well below pentatri. Ikosarakt1 (talk) 10:18, February 14, 2013 (UTC) :I was joking and making a reference to . FB100Z • talk • 17:42, February 14, 2013 (UTC) Since \(n = 2\), \(k_{i + 1} = n \uparrow^{k_i} n = 2 \uparrow^{k_i} 2 = 4\). So \(\widetilde{R} = 4\)? FB100Z • talk • 22:37, February 18, 2013 (UTC) It turns out that. Btw, there are some disambiguation with \(n¥ = {}^{n!}(n\$) \uparrow \cdots \uparrow {}^{2!}(2\$) \uparrow {}^{1!}(1\$)\). What index means here, tetration of superfactorials or number of up-arrows? Ikosarakt1 (talk) 22:49, February 18, 2013 (UTC) :Rucker's notation \(^ba\) has always bothered me a little. I'll parenthesize the tetrations to clear that up. FB100Z • talk • 23:02, February 18, 2013 (UTC) :There are a few mistakes into the definition, because widetilde{R} is defined by recursion, starting from k(n) where you can assume n=2 (even if BOX_M~ is a proof-tool, so there is not a strict constraint on "n"). R~ is an hyperoperator that is defined considering that k(1):=(Mn£(An£))!, k(2)=2\uparrow^{k_i} 2 and so on. When we reach k(k1), we step-up to the second level... repeating this process over and over we get (k(k(...(k1)))) (with G£ copies of k). At this point, we have to repeat the process G£-1 times to reach R~. :For comparison, 2 \uparrow^{k(k_1)} 2 > G (Graham's number). :My apologies for the text format, but I haven't enough time to rewrite it in the right form. :SPIqr (talk) 01:57, February 19, 2013 (UTC) ::I suspected that there were some issues with my translation (which was a combination of Google Translate and wanton guessing). FB100Z • talk • 03:06, February 19, 2013 (UTC) I've just checked the original book and I've discovered what's the problem: the original article was about hyperoperators only, then it has been added the Graham's number comparison into the funny paper, so it was implicit (even if not cleary stated) that "n" have to assume the value of the BOX_M~ side (BOX_M~ is defined as a multidimentional numbers hypersolid). The ridicolus part is that the side hasn't been closed (its stated that n would be equal to G£ but it not clear enough), so it remains an open box and, assuming n=2, R~ crashes to a very small value (good call). Due to this misunderstooding, for the BOX_M~ creation, n has been set to G£. I think that the new version of the paper would be clear enough for a unique definition of BOX_M~. In this way, its value will be fixed and it could be compared to other numbers belonging to the same growth hierarchy. P.S. The errors into the paper have been fixed now... this is a classical obstacle that you find trying to blow the dust of something that you have written months before, thinking to a different topic (the original BOX_M~ creation reason was a philosphical question related to recreational logics). All the best SPIqr (talk) 03:18, February 19, 2013 (UTC) I added BOX_M~ to my number list thing. Is the analysis correct? WikiRigbyDude (talk) 16:25, June 23, 2014 (UTC) :Yes, and generally, the good trick in bounding numbers with salad definitions is taking the fastest-growing function in the definition and iterating over it. Ikosarakt1 (talk ^ ) 05:59, June 24, 2014 (UTC) Why do we allow this on mainspace Why do we allow that salad here?There is no use in this number.Boboris02 (talk) 17:12, February 20, 2017 (UTC) :We allow it because it has an external source and somebody decided to create an article for the number. There's no other reasons here, even if it's a salad number. -- ☁ I want more ⛅ 13:25, February 21, 2017 (UTC) ::...except that it's an UTTERLY good example of a salad number. 17:13, November 17, 2017 (UTC)